Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2022-54-5
Brahim Mittou, Abdallah Derbal
Recently, the authors gave asymptotic formulas for L(s, χ), which associated with a primitive Dirichlet character χ, in terms of the generalized Bernoulli numbers. In this paper, based on the aforementioned asymptotic formulas we describe a method for calculating Dirichlet L-functions that can be used to validate the generalized Riemann hypothesis up to a height T > 0. Our method is a refinement of the one presented by Davies and Haselgrove.
本文利用广义伯努利数给出了与原始狄利克雷特征χ相关的L(s， χ)的渐近公式。在本文中，基于上述渐近公式，我们描述了一种计算Dirichlet l -函数的方法，该方法可用于验证高度T > 0的广义黎曼假设。我们的方法是对Davies和Haselgrove提出的方法的改进。
{"title":"Method for calculating Dirichlet L-functions","authors":"Brahim Mittou, Abdallah Derbal","doi":"10.20948/mathmontis-2022-54-5","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-54-5","url":null,"abstract":"Recently, the authors gave asymptotic formulas for L(s, χ), which associated with a primitive Dirichlet character χ, in terms of the generalized Bernoulli numbers. In this paper, based on the aforementioned asymptotic formulas we describe a method for calculating Dirichlet L-functions that can be used to validate the generalized Riemann hypothesis up to a height T > 0. Our method is a refinement of the one presented by Davies and Haselgrove.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114078105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2022-54-3
O. Elong
We prove LP boundedness of a class of semiclassical Fourier integral operators defined by smooth phase function and semiclassical rough symbols on the spatial variable 𝑥. We also consider a spacial case of ℎ -pseudodifferential operators.
{"title":"On the LP boundedness of h-Fourier integral operators with rough symbols","authors":"O. Elong","doi":"10.20948/mathmontis-2022-54-3","DOIUrl":"https://doi.org/10.20948/mathmontis-2022-54-3","url":null,"abstract":"We prove LP boundedness of a class of semiclassical Fourier integral operators defined by smooth phase function and semiclassical rough symbols on the spatial variable 𝑥. We also consider a spacial case of ℎ -pseudodifferential operators.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128165247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2023-56-4
M. Bouderbala
The gcd-sum function is one of the most important functions that has been studied by many researchers in recent years (Broughan, Bordellès, etc.). The gcd-sum function appears in a specific lattice point problem, where it can be used to estimate the number of integer coordinate points under the square root curve. In this paper, we give an average order of the gcd-sum function over the set of squares.
{"title":"On the average order of the gcd-sum function over the set of square integers","authors":"M. Bouderbala","doi":"10.20948/mathmontis-2023-56-4","DOIUrl":"https://doi.org/10.20948/mathmontis-2023-56-4","url":null,"abstract":"The gcd-sum function is one of the most important functions that has been studied by many researchers in recent years (Broughan, Bordellès, etc.). The gcd-sum function appears in a specific lattice point problem, where it can be used to estimate the number of integer coordinate points under the square root curve. In this paper, we give an average order of the gcd-sum function over the set of squares.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"2012 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128896129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1900-01-01DOI: 10.20948/mathmontis-2023-56-8
Zaur Rasulov, U. Yesil
Beam-like structures are widespread but essential systems that have been extensively studied for centuries. Although several proposed solutions are effective, the time consumption and the difficulty of reconstructing the problem are the major disadvantages of these methods. This paper offers a new methodology for finding solutions to beam problems based on Machine Learning and Neural Networks with different optimization algorithms. Various regression models are compared on numerically stimulated Euler-Bernoulli beam modelling.
{"title":"Machine learning and neural networks based approach for deflection prediction of Euler-Bernoulli beam equations","authors":"Zaur Rasulov, U. Yesil","doi":"10.20948/mathmontis-2023-56-8","DOIUrl":"https://doi.org/10.20948/mathmontis-2023-56-8","url":null,"abstract":"Beam-like structures are widespread but essential systems that have been extensively studied for centuries. Although several proposed solutions are effective, the time consumption and the difficulty of reconstructing the problem are the major disadvantages of these methods. This paper offers a new methodology for finding solutions to beam problems based on Machine Learning and Neural Networks with different optimization algorithms. Various regression models are compared on numerically stimulated Euler-Bernoulli beam modelling.","PeriodicalId":170315,"journal":{"name":"Mathematica Montisnigri","volume":"154 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115194942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：